We use SINDy to just fit the spatial coordinates and set \(\omega =-2\)  and \(\alpha =0.1\) . We refer the interested reader to [1]} for the detailed derivation of the constraints, but for our purposes, the relevant fact is simply that the potential function imposes a set of equality constraints on \(\Xi \) . We can then use a vectorized representation of the coefficients \(\bar{\xi }\) , and add \(A \bar{\xi } = b\)  to the MIO model where \(A, \ b\)  are based on the partial derivatives of \(V(x, y)\) . Because these constraints extend between dimensions, we use the joint formulation REF  to fit \(x\)  and \(y\)  simultaneously.
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